MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING

CAMBRIDGE, MASSACHUSETTS 02139

2.002 MECHANICS and MATERIALS II SPRING 2004

SUPPLEMENTARY NOTES c L. Anand and D. M. Parks

DEFECTFREE FATIGUE

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1. INTRODUCTION

Fatigue Failure is the failure of components under the action of repeated fluctuating stresses or strains. The word fatigue was introduced in the 1840s and 1850s in connection with such failures which occurred in the then rapidly developing railway industry. It was found that railroad axles failed regularly at shoulders, and that these failures appeared to be quite different from failures associated with monotonic testing.

Fatigue failure may be defined as a process in which there is progressive, localized, permanent microstructural change occurring in a structure when it is subjected to boundary conditions which produce fluctuating stresses and strains at some material point or points. These microstructural changes may culminate in the formation of cracks and their subsequent growth to a size which causes final fracture after a sufficient number of stress or strain fluctuations.

The adjective progressive implies that the fatigue process occurs over a period of time or usage. The occurrence of a fatigue failure is often very sudden, with no external warning; however, the mechanisms involved may have been operating since the beginning of the time when the component or structure was put to use.

The adjective localized implies that the fatigue process operates preferentially at specific local areas, rather than homogeneously throughout the body. These vulnerable areas can have high local strains and stresses due to stress and strain concentrations caused abrupt changes in geometry and/or material imperfections.

The phrase permanent microstructural changes emphasizes the central role of cyclic plastic deformations in causing irreversible changes in the substructure. Countless investigations have established that fatigue results from cyclic plastic deformation in every instance, even though the structure as a whole is practically elastic. A small plastic strain excursion applied only once does not cause any substantial changes in the substructure of materials, but multiple repetitions of very small plastic strains lead to cumulative damage ending in fatigue failure. We note that although fatigue is popularly associated with metallic materials, it can occur in all engineering materials capable of undergoing plastic deformation. This includes polymers, and composite materials with plastically deformable phases. Plastically nondeformable materials such as glasses and ceramics, in which deformations at ambient temperatures are truly elastic everywhere, do not fail by fatigue due to repeated stresses. However, recent data has shown that polycrystalline ceramics can exhibit fatigue crack growth under certain circumstances. Such a process is still consistent with our definition in the sense that local irreversible deformation at the crack tip associated with processes such as microcracking, frictional sliding, particle detachment and crack face wedging are involved in the fatigue process. Furthermore, these local mechanisms in brittle materials can give rise to macroscopic

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behavior which is phenomenologically similar to plasticity.

There are currently two principal methodologies for design and maintenance to resist fatigue failure of components, defectfree and defecttolerant. These two approaches are based on the how the crack size a in a component increases with the number of stress or strain cycles N imposed on the component.

1. DEFECTFREE DESIGN AND MAINTENANCE APPROACH:

The defectfree approach is mostly used to design small components which are not safety critical.

In this approach, it is assumed that no cracklike defects preexist. That is, the initial crack size a is taken to be zero. Figure 1 shows a schematic of the behavior of crack size, a, versus the number of applied cycles of loading, N , for an initially uncracked component. The number of cycles to fatigue failure of the component is denoted by Nf (the subscript f here refers to failure) . The total number of loading cycles to failure may be conceptually decomposed as

Nf = Ni + Np, (1)

where Ni is the number of cycles required to initiate a fatigue crack, and Np is the number of cycles required to propagate a crack to final fracture after it has initiated. Of course, the precise boundary between these two regions depends on the value chosen for the initiation crack size, ai.

Although the total fatigue life, within the defectfree approach, consists of an initiation life and a propagation life, fatigue failure is often said to have occurred when a crack has initiated. This simplification is adopted since usually Np Ni; in such case, the propagation life, Np, can be neglected in comparison to the initiation life, Ni, and total fatigue life, Nf , is approximated as

Nf Ni.

Further, a fatigue crack in a typical engineering component is often said to have initiated when it is readily visible to the naked eye, that is ai 1mm. Of course, specific circumstances (e.g., small components) may require adoption of other, more appropriate, definitions of fatigue initiation and initiation crack size.

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Crack Size, a

Number of cycles, N

x

Ni Np

Nf

ai

ac

Figure 1: Schematic of crack length, a, versus number of loading cycles, N , in an initially uncracked component.

The defectfree methodology is usually subdivided into two subcategories.

(a) Highcycle fatigue:

Highcycle fatigue is associated with local cyclic stresses which are of sufficiently small magnitude so that they produce predominantly elastic straining, and the resulting fatigue life exceeds 104 cycles. Examples of components designed in consideration of highcycle fatigue in clude most rotating and vibrating members.

(b) Lowcycle fatigue:

Lowcycle fatigue is associated with local cyclic stress levels which are sufficiently large so that significant cyclic plastic straining occurs, and the resulting fatigue life is less than 104 cycles. Example applications that are designed in consideration of lowcycle fatigue include core components of nuclear reactors and gas turbine engines, which

in their lifetime may see a limited number of modestly large cyclic straining

events associated with startup and shutdown cycles. Other application areas

include design of many ground vehicle components which are occasionally

subjected to overloads sufficient to cause local yielding at notch roots, etc.

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0

Crack Size, a

Number of cycles, N

ai

xac

ad

NpNf =

2. DEFECTTOLERANT DESIGN AND MAINTENANCE APPROACH:

If the potential costs of a structural fatigue failure in terms of human life and dollars is very high, then the design of such engineering components and structures is often [more conservatively] based on:

(a) The assumption that all fabricated components and structures contain a preexisting population of cracks of an initial size ai. This initial size should be taken to be the larger of (i) the largest actuallydetected initial crack, and (ii) the detectionlimit crack size, ad, which is the largest crack size that can escape detection by the adopted nondestructive testing (NDT) method. Because it is assumed in this approach that a crack preexists, Ni = 0, and therefore Nf = Np. See Figure 2.

(b) The requirement that none of the population of assumed preexisting cracks be permitted to grow to a critical size during the expected service life of the part or structure. Normally, this requires the selection of inspection intervals within the service life. In application of such defecttolerant strategies, it is also assumed that the initial location and orientation of the [typically not actually detected] defect is the worst possible; that is, that it occurs at the point of highest cyclic stress, and is oriented perpendicular to the cyclic tensile stress range at that location.

Figure 2: Schematic of crack length, a, versus number of cycles, N , in a component with an initial crack size ai. The initial crack size is typically taken to be the largest crack size, ad, that can escape detection by NDT techniques.

The major aim of the defecttolerant approach to fatigue is to reliably predict

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the growth of preexisting cracks of specified initial size, ai, shape, location, and orientation in a structure subjected to prescribed cyclic loadings. Providing this goal can be achieved, then inspection and service intervals can be established such that cracks should be readily detectable well before they have grown to near critical size, ac.

The defecttolerant approach to fatigue is typically used in the design and maintenance of large, fabricated structures such as aircraft, ships, pressure vessels, etc., where welds are likely sites for initial defects, and the large size of the components may permit substantial subcritical crack growth, so that the enlarged defect can be detected and repaired or replaced well before it reaches a critical dimension. Defecttolerant strategies are also appropriate to safetycritical applications of components of arbitrary size.

Within the scope of a defecttolerant approach, two subapproaches may be identified. One of these is termed failsafe design. In this case, the basic concept is that a structure should possess a sufficient redundancy of elements or components to provide assurance that, for a specified operating load, the failure or fracture of any single element or component will not lead to catastrophic failure of the structural